An experiment consists of selecting 10 people at random and

An experiment consists of selecting 10 people at random and recording the day of the week that each person was born. What is the probability that exactly 2 of these people were born on a Monday?

Solution

There are 7^10 ways that these people have birthdays.

There are 10C2 ways to choose wich two have mondays, and then, for the remaining 8, they can choose 6 days, thus, in 6^8 ways.

Thus,

P(exactly 2 mondays) = [10C2 * 6^8] / [7^10]

= 0.267572895 [answer]